Let us make sense of it like this:
Each cardinal > 1 is defined by a recursion of two basic states of Distinction, which are:
1) Superposition of Ids (the id of a given element is not crisp).
Superposition of ids of a given element is notated as
n , where
n = 2 → ∞
2) Crisp id of the given element is notated as
n where
n=1
Each serial observation of some Organic Number can be shown by first using the partition of some cardinal, for example, the ordered partitions of cardinal 4 are:
Now by using Distinction as the leading property of the research, we look for the association of crisp and non-crisp ids of each element, by using recursion, where each recursion is closed under some cardinal, where some partition is a collection of cardinals, for example:
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Under the partition 1 1 1 1, we have exactly 1 Distinct form of non-crisp ids, notated as:
Code:
1 1 1 1 = partition
([U]4[/U],[U]4[/U],[U]4[/U],[U]4[/U]) = distinction
where
4 means that each element (under cardinal 1) has a superposition of 4 ids.
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Under the partition 2 1 1, we have exactly 2 Distinct forms of non-crisp or crisp ids, notated as:
Code:
2 1 1 = partition
([U]2[/U],[U]2[/U],[U]4[/U],[U]4[/U]) = distinction
where
4 means that each element (under cardinal 1) has a superposition of 4 ids, and
2 means that each element (under cardinal 2) has a superposition of 2 ids.
Code:
2 1 1 = partition
([U]1[/U],[U]1[/U],[U]4[/U],[U]4[/U]) = distinction
where
4 means that each element (under cardinal 1) has a superposition of 4 ids, and
1 means that each element (under cardinal 2) has a crisp id.
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Under the partition 2 2, we have exactly 3 Distinct forms of non-crisp or crisp ids, notated as:
Code:
2 2 = partition
([U]2[/U],[U]2[/U],[U]2[/U],[U]2[/U]) = distinction
where
2 means that each element (under cardinal 2) has a superposition of 2 ids.
Code:
2 2 = partition
([U]1[/U],[U]1[/U],[U]2[/U],[U]2[/U]) = distinction
where
2 means that each element (under cardinal 2) has a superposition of 2 ids, and
1 means that each element (under cardinal 2) has a crisp id.
Code:
2 2 = partition
([U]1[/U],[U]1[/U],[U]1[/U],[U]1[/U]) = distinction
where
1 means that each element (under cardinal 2) has a crisp id.
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Under the partition 3 1, we have exactly 3 Distinct forms of non-crisp or crisp ids, notated as:
Code:
3 1 = partition
([U]3[/U],[U]3[/U],[U]3[/U],[U]1[/U]) = distinction
where
3 means that each element (under cardinal 3) has a superposition of 3 ids, and
1 means that 1 element (under cardinal 1) has a crisp id.
Code:
3 1 = partition
2 1,1 = partition
([U]2[/U],[U]2[/U],[U]1[/U],[U]1[/U]) = distinction
where
2 means that each element (under cardinal 2, which is under cardinal 3) has a superposition of 2 ids,
1 means that 1 element (under cardinal 1, which is under cardinal 3) has a crisp id, and another
1 means that 1 element (under cardinal 1) has a crisp id.
Code:
3 1 = partition
2 1,1 = partition
([U]1[/U],[U]1[/U],[U]1[/U],[U]1[/U]) = distinction
where
1 means that each element (under cardinal 2, which is under cardinal 3) has a crisp id, another
1 means that 1 element (under cardinal 1, which is under cardinal 3) has a crisp id, and another
1 means that 1 element (under cardinal 1) has a crisp id.
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4=4 and has 0 partitons.
Organic Number 4 is the result of universe ____\. , such that 4 = _____ and 1 = . , gathered by ______
